A three-dimensional computational method for blood flow in the heart. I: Immersed elastic fibers in a viscous incompressible fluid
The heart wall is modelled as a viscous incompressible fluid that contains elastic fibres. The fluid has mass and volume whereas the fibre is assumed to transmit stress only and does not have mass or volume. The appropriate three dimensional time dependent equations are established. These consist of the Navier-Stokes equations in the fluid, equations for the fibre and a set of linking equations. A suitable numerical method is developed for solving the equations and this is then implemented on a large computer. There is a detailed discussion of this process including such topics as vectorization and the use of the central memory of the computer. As a preliminary to considering the behaviour of the heart the equations and method of solution are used to solve the problem of the vibration of a fibre wound toroidal tube. Numerical results are presented in graphical form. This is an impressive paper covering a wide spread of mathematical techniques with direct application to a practical problem.
scientific article; zbMATH DE number 4095150